First principles theory of ground and excited states of correlated light-matter systems in the non-perturbative regime

Ultra-strong coupling between light and matter promises to bring about new means to control material properties, concepts for manipulating light at the atomic scale, and insights into quantum electrodynamics (QED). Thus, there is a need to develop quantitative theories of QED phenomena in complex electronic and photonic systems. Here, we develop a new variational paradigm to analyze ultra-strongly coupled light-matter systems which gives ground and excited state information as well as real-space information about electromagnetic fields as they are modified by strong light-matter coupling. Our method gives highly accurate energies for both ground and excited states for systems with many emitter levels and many photon modes that go beyond solvable model systems in quantum optics. One important result is that we arrive at the first theory of Lamb shifts and Casimir-Polder forces in the ultrastrong coupling regime, which reveals new saturation effects that strongly suppress energy shifts as light-matter coupling grows. Beyond accurate calculation of ground and excited state energies, our results will give accurate descriptions of light-emission phenomena in the non-perturbative regime.